Model

Overview

Our film is a potential candidate competing against cling film on the market, so it needs to meet certain requirements in terms of structural strength. On the other hand, our film has a great advantage in antibacterial properties, so we also need to characterize its antibacterial performance. The overall performance of our film consists of mechanical performance and antibacterial performance. As a result, we built up two sub-models to estimate the two scores separately, and then added the two scores up to obtain an integrated score. The area of film is fixed at 64 square centimeters^[1].

Model to represent antibacterial properties of double layer film

Introduction

The first sub-model describes the antibacterial score with two factors: the concentration of ε-PLL and the drying temperature. As the main antibacterial substance of our product, increasing concentration of ε-PLL significantly enhances the antibacterial ability of the film at low concentrations. However, due to saturation effects and limited film carrying capacity, there is a limit to its antibacterial ability at high concentrations. On the other hand, water content also influences the antibacterial properties of our product. Too high water content of the film will lead to insufficient attraction to ε-PLL, unable to carry enough antibacterial substances, while too low water content will affect the ionization of PLL, making it unable to generate antibacterial substances.

Model Design

The shape of is an S-shaped curve with a saturation effect, which can be described by a logistic function. The concentration ranges from 0.1% to 2%, and the antibacterial score gradually increases and then levels off as concentration rises^[2].

For the temperature factor, the drying temperature influences bacterial inhibition efficiency: excessively low temperature results in incomplete drying, while overly high temperature decreases antibacterial activity.

Both factors are multiplied to obtain the antibacterial score, with the final result normalized to the range 0–1.

Fig1. The sub-model of antibacterial score

Model to represent physical properties of double layer film

Introduction

The second sub-model describes the mechanical score with two major factors: the concentration of ε-PLL and the drying time. Because the ε-PLL carries positive ions, it may increase the polymerization degree of sodium alginate or chitosan through crosslinking, thereby changing their mechanical strength. A low concentration will make the film more flexible but less resistant to shear, while a high crosslinking degree will make the film harder but very fragile. The effect of drying time on the mechanical properties of the film is reflected in the water content. Excessive water content can lead to the inability to form a film or extremely strong flexibility, while insufficient moisture content can easily cause the film to break.

Model Design

For the concentration of ε-PLL. A small amount of ε-PLL (around 0.4%) can enhance the flexibility and toughness of the film^[3], while excessive addition significantly reduces mechanical performance. Therefore, it follows a unimodal curve that peaks at low concentration and declines sharply at higher levels.

The drying time also plays a crucial role in determining mechanical properties. If the film is dried for too short a period^[4], it cannot form properly due to high residual moisture. Conversely, an excessively long drying time makes the film overly dry and brittle. Thus, exhibits an optimal range, where mechanical performance reaches its maximum. The final mechanical score is obtained by combining these two factors and is also normalized to the range 0–1^[5].

The final mechanical score is obtained by combining these two factors and is also normalized to the range 0–1.

Fig2. The sub-model of mechanical score

Model of final score

Introduction

After independently constructing models for antibacterial and mechanical properties, we measured the specific performance of our product's cling film. Because the weighting of antibacterial performance and mechanical performance is different in the overall score, we need to multiply them by different parameters.

Model design

The overall performance score of the film, , is obtained by combining the antibacterial score and the mechanical score . Each sub-model is independently normalized to the range of 0–1, so that their contributions can be directly added without further weighting.

Where

It is an integrated function that describes the impact of ε-PLL concentration on mechanical strength and antibacterial effect, while representing the drying time and drying temperature effect with an optimal range.

Since both sub-models are constrained to values between 0 and 1, the integrated score ranges from 0 to 2. This integrated model provides a balanced evaluation of both antibacterial and mechanical performances, enabling the identification of optimal preparation conditions for the film.

Fig3. The integrated model of total score

Feasibility analysis of the model

To indicate mechanical performance, we conducted a tensile strength test. We cut the film into strips. The sizes of the strips in one of our tests are as follows:

We secured the strips vertically on a texture analyzer probe. The installation parameters are as follows: a return distance of 60 mm, a speed of 1 mm/s, an effective elongation distance of 80 mm, and a trigger force of 5 N. We then calculated the film’ tensile strength using the following equation:

Where Ts is the tensile strength (MPa), F is the maximum tensile force when the sample fractures (N), and S is the cross-sectional area of the sample (width*thickness; )

Fig4. Mechanical test with the variable of drying time

To quantify the antibacterial performance, we used Corynebacterium glutamicum representing and E. coli representing Gram-positive and Gram-negative bacteria respectively to conduct inhibition zone test. First, we divided our film samples into experimental group and controlling group, and then cut them into pieces. After pouring nutrient agar and apply broth culture added with bacteria to petri dishes, we placed pieces of film from two groups in these petri dishes and put the petri dishes into the incubator at 37 ℃ for 24 h. Finally, we collected the data in optical density experiment to determine the amount of bacteria left. The antibacterial rate was calculated and averaged in the following way:

Where At is the optical density of the bacterial suspension co-cultured with the antibacterial film, and Ac is the optical density of the suspension co-cultured with a control film. 

Result

The result indicates that our model fits the calculated score and suggests the overall tendency of integrated performance. The optimal drying time, concentration of ε-PLL and drying temperature fall narrowly in the range expected by our model. To be specific, the ultimate optimal drying time is between 4 to 5 hours; the optimal concentration of ε-PLL is between 0.3% to 0.4%; the optimal drying temperature is about 40 to 60 ℃, according to experiment results. This data can be predicted by our model, confirming the feasibility of our model. Small deviation may result from the measuring inaccuracy and the limitation of equipment, which can be improved in the future.

References